Homological Groups, Spanning Forests and Membrane Computing

In this paper we present a new way to determine the geometrical objects associated to the Homology groups of a 2D-digital binary image. In fact, using Membrane Computing with techniques of spanning forests, we are able to define a parallel algorithm which calculates not only the Betti numbers, but also the geometric objects which generate these holes

Bioinspired parallel 2D or 3D skeletonization

Algebraic Topology has been proved to be an useful tool to be used in image processing. In this case we will borrow some elements from Algebraic Topology in order to show a parallel algorithm for thinning a binary 3D image respecting its shape information. The parallelization of the thinning algorithm is based on Membrane Computing. This research area has already been proved to be useful in the development of parallel image processing algorithms. We present here the main guidelines of the algorithms along with a slight introduction about some basic required knowledge about Algebraic Topology and Membrane Computing

Semantics of deductive databases with spiking neural P systems

The integration of symbolic reasoning systems based on logic and connectionist systems based on thefunctioning of living neurons is a vivid research area in computer science. In the literature, one can findmany efforts where different reasoning systems based on different logics are linked to classic artificialneural networks. In this paper, we study the relation between the semantics of reasoning systems basedon propositional logic and the connectionist model in the framework of membrane computing, namely,spiking neural P systems. We prove that the fixed point semantics of deductive databases without nega- tion can be implemented in the spiking neural P systems model and such a model can also deal withnegation if it is endowed with anti-spikes and annihilation rules

Semantics of Deductive Databases in a Membrane Computing Connectionist Model

The integration of symbolic reasoning systems based on logic and connectionist systems based on the functioning of living neurons is a vivid research area in computer science. In the literature, one can found many e orts where di erent reasoning systems based on di erent logics are linked to classic arti cial neural networks. In this paper, we study the relation between the semantics of reasoning systems based on propositional logic and the connectionist model in the framework of membrane computing, namely, spiking neural P systems. We prove that the xed point semantics of deductive databases and the immediate consequence operator can be implemented in the spiking neural P systems model

Semantics of Deductive Databases in a Membrane Computing Connectionist Model

The integration of symbolic reasoning systems based on logic and connectionist systems based on the functioning of living neurons is a vivid research area in computer science. In the literature, one can found many e orts where di erent reasoning systems based on di erent logics are linked to classic arti cial neural networks. In this paper, we study the relation between the semantics of reasoning systems based on propositional logic and the connectionist model in the framework of membrane computing, namely, spiking neural P systems. We prove that the xed point semantics of deductive databases and the immediate consequence operator can be implemented in the spiking neural P systems model

Region-based segmentation of 2D and 3D images with tissue-like P systems

Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform computations by applying a finite set of rules in a synchronous, maximally parallel way. In this paper, we develop a variant of P-system, called tissue-like P system in order to design in this computational setting, a region-based segmentation algorithm of 2D pixel-based and 3D voxel-based digital images. Concretely, we use 4-adjacency neighborhood relation between pixels in 2D and 6-adjacency neighborhood relation between voxel in 3D for segmenting digital images in a constant number of steps. Finally, specific software is used to check the validity of these systems with some simple examples

Solving the 3-COL Problem by Using Tissue P Systems without Environment and Proteins on Cells

The 3-COL problem consists on deciding if the regions of a map can be coloured with only three colors bearing in mind that two adjacent regions must be coloured with di erent colors. It is a NP problem and it has been previously used in complexity studies in membrane computing to check the ability of a model for solving problems of such complexity class. Recently, tissue P systems with proteins on cells have been presented and its ability to solve NP-problems has been proved, but it remained as an open question to know if such model was still able to solve such problems if the environment was removed. In this paper we provide an a rmative answer to this question by showing a uniform family of tissue P systems without environment and with proteins on cells which solves the 3-COL problem in linear time

Image Segmentation using Tissue-like P Systems with Multiple Auxiliary Cells

We present a solution of the segmentation problem using a distributed, non deterministic and parallel computational model known as tissue-like P systems. We present a new technique to segment images with respect to the algorithm appeared in [1], where we use multiple auxiliary cells and not only one

Obtaining Homology Groups in Binary 2D Images Using P Systems

Membrane Computing is a new paradigms inspired from cellular communication. We use in this paper the computational devices called P systems to calculate in a general maximally parallel manner the homology groups of binary 2D images. So, the computational time to calculate this homology information only depends on the thickness of them.Junta de Andalucía FQM-296Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08-TIC-04200Ministerio de Educación y Ciencia MTM2006-03722Junta de Andalucía PO6-TIC-0226

Designing Tissue-like P Systems for Image Segmentation on Parallel Architectures

Problems associated with the treatment of digital images have several interesting features from a bio-inspired point of view. One of them is that they can be suitable for parallel processing, since the same sequential algorithm is usually applied in different regions of the image. In this paper we report a work-in-progress of a hardware implementation in Field Programmable Gate Arrays (FPGAs) of a family of tissue-like P systems which solves the segmentation problem in digital images.Ministerio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-04200Junta de Andalucía PO6-TIC-02268Ministerio de Educación y Ciencia MTM2009-1271